Notes 5.4 HL and CPCTC.pdf - Notes 5.4 HL and CPCTC There...

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Notes: 5.4 HL and CPCTC There is one final method of proving that 2 triangles are congruent. It is called Hypotenuse-leg. Complete each congruence statement, use SSS, SAS, ASA, AAS or HL. 1. __________ by________ 2. __________ by________ DRF by AAS GFD by HL HL Hypotenuse-Leg Need 3 parts to show that the triangles are congruent by HL Right triangles The hypotenuses are congruent One pair of legs are congruent. R D F Y A W R D F G R D F G If: and are right ̅̅̅̅ ̅̅̅̅ and ̅̅̅̅̅ ̅̅̅̅ Then: by HL Mark any common sides and vertical angles congruent. Then determine which method was used to prove the triangles congruent. R D F G Sometimes it is easier to look at 1 triangle when trying to determine which method was used to prove the triangles congruent. The triangle is right and the legs were marked congruent. The hypotenuse is a reflexive side. R D F G Leg Remember to match the triangles in the correct order.
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3. __________ by________ 4. _________ by________ FDG by SSS SZY by HL 5. __________ by________ 6. __________ by________ AXO by AAS GTK by SAS CPCTC stands for C
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Unformatted text preview: orresponding P arts of C ongruent T riangles are C ongruent. CPCTC is the final step in many proofs used to show that “ extra ” parts of the triangles are congruent. You will first need to prove that the triangles are congruent, and then using CPCTC you can state that the extra parts are also congruent. R D F G S Y Z W A X O R N G K F T P Vertical angles are congruent. 1. Given: Prove: 2. Given: is the midpoint of ̅̅̅̅ and ̅̅̅̅ (Look at next page for solution) Prove: 1. 1. Given 2. 2. 3. 3. A D E F B C 1. 1. Given 2. 2. SSS 3. 3. CPCTC A D E F B C Mark the given information in the diagram. After the triangles are congruent, you can state that the extra parts are congruent. C A S T R 1 2 1. is the midpoint of ̅̅̅̅ and ̅̅̅̅ 1. Given 2. 2. Definition of midpoint 3. 3. 4. 4. 5. 5. 2. Given: is the midpoint of ̅̅̅̅ and ̅̅̅̅ Prove: Mark the congruent segments from the midpoint. C A S T R 1 2 1. is the midpoint of ̅̅̅̅ and ̅̅̅̅ 1. Given 2. 2. Definition of midpoint 3. 3. Vertical angles are congruent 4. 4. SAS 5. 5. CPCTC...
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